What is the limit as x approaches 0 of (x+x^2)/x ?

The limit as x approaches 0 of (x+x^2)/x is 1

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limit as x approaches 0 of (x+x^2)/x

x \to 0 lim (\frac{x + x ^{2}}{x})

1

Solution steps

x \to 0 lim (\frac{x + x ^{2}}{x})

Simplify

\frac{x + x ^{2}}{x} : 1 + x

= x \to 0 lim (1 + x)

Plug in the value

x = 0

= 1 + 0

Simplify

= 1

x \to 0 lim (\frac{0}{2 x})

x \to 0 + lim ((2^{x} - 1)^{x})

x \to 0 lim (\frac{2 x}{3})

x \to 1 lim (\frac{x ^{2} - 3}{x - 1})

x \to 2 lim (\frac{3}{( x + 2 )})

What is the limit as x approaches 0 of (x+x^2)/x ?
The limit as x approaches 0 of (x+x^2)/x is 1